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RWHG

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Random walks on hyperbolic groups

The project lies at the confluent of different mathematical fields: probability theory, algebra, and geometry. There is a contribution of A. V. Vershik in a special Springer volume about the future of mathematics in the 21st centu... ver más

30/11/2010

AMU

157K€

Presupuesto del proyecto: 157K€

Líder del proyecto

UNIVERSITE DAIX MARSEILLE No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

Ver 2 Participantes

Financiación concedida El organismo FP7 notifico la concesión del proyecto el día 2010-11-30 No tenemos la información de la convocatoria

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2 Participantes

AMU

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Líder del proyecto

UNIVERSITE DAIX MARSEILLE No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 157K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto The project lies at the confluent of different mathematical fields: probability theory, algebra, and geometry. There is a contribution of A. V. Vershik in a special Springer volume about the future of mathematics in the 21st century that points out the prospects and challenges that are comprised in the interplay of probability theory and algebra. Here random walk theory, a branch of probability theory, plays a mayor role. There are two points of view to look at the relation between probability theory, algebra, and geometry. The probabilistic viewpoint concerns all questions regarding the impact of the underlying structure on the behavior of the corresponding random walk. Typically one is interested in transience/recurrence, spectral radius, rate of escape, and central limit theorems. On the other hand, random walks are a useful tool to describe the structure that underlies the random walk. In particular, algebraic and geometric properties can be classified due to the behaviour of the corresponding random walks. The project falls exactly into this topic: we will study random walks on hyperbolic groups. The objectives are to prove a central limit theorem for random walks on hyperbolic groups and provide geometric interpretations of the asymptotic variance. This will arise from a geometric perspective in the flavour of the interpretation for the rate of escape in terms of entropy and requires deeper knowledge of hyperbolic geometry together with inspiration and new ideas. The project will settle the ground for future collaboration, not only between France and Germany but also on an European level, since the host institute and the applicant have strong European contacts. Furthermore, the project can be seen as a continuation and complement of the existing Marie Curie contract ``European Training Courses and Conferences in Group Theory''.

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